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@@ -41,7 +41,7 @@ \title{\urusi mft} \author{Jaron Kent-Dobias} -\author{Mike Matty} +\author{Michael Matty} \author{Brad Ramshaw} \affiliation{Laboratory of Atomic \& Solid State Physics, Cornell University, Ithaca, NY, USA} @@ -75,6 +75,36 @@ \item Talk about more cool stuff like AFM C4 breaking etc \end{enumerate} +The study of phase transitions is a central theme of condensed matter physics. In many +cases, a phase transition between different states of matter is marked by a change in symmetry. +In this paradigm, the breaking of symmetry in an ordered phase corresponds to the condensation +of an order parameter (OP) that breaks the same symmetries. Near a second order phase +transition, the physics of the OP can often be described in the context of Landau-Ginzburg +mean field theory. However, to construct such a theory, one must know the symmetries +of the order parameter, i.e. the symmetry of the ordered state. + +One quintessential case where the symmetry of an ordered phase remains unknown is in \urusi. +\urusi is a heavy fermion superconductor in which superconductivity condenses out of a +symmetry broken state referred to as hidden order (HO) [cite pd paper], and at sufficiently +large [hydrostatic?] pressures, both give way to local moment antiferromagnetism. +Despite over thirty years of effort, the symmetry of the hidden order state remains unknown, and +modern theories [big citation chunk] propose a variety of possibilities. +Many [all?] of these theories rely on the formulation of a microscopic model for the +HO state, but without direct experimental observation of the broken symmetry, none +have been confirmed. + +One case that does not rely on a microscopic model is recent work [cite RUS paper] +that studies the HO transition using resonant ultrasound spectroscopy (RUS). +RUS is an experimental technique that measures mechanical resonances of a sample. These +resonances contain information about the full elastic tensor of the material. Moreover, +the frequency locations of the resonances are sensitive to symmetry breaking at an electronic +phase transition due to electron-phonon coupling [cite]. Ref. [RUS paper] uses this information +to place strict thermodynamic bounds on the symmetry of the HO OP, again, independent of +any microscopic model. Motivated by these results, in this paper we consider a mean field theory +of an OP coupled to strain and the effect that the OP symmetry has on the elastic response +in different symmetry channels. Our study finds that a single possible OP symmetry +reproduces the experimental strain susceptibilities, and fits the experimental data well. + The point group of \urusi is \Dfh, and any coarse-grained theory must locally respect this symmetry. We will introduce a phenomenological free energy density in three parts: that of the strain, the order parameter, and their interaction. The most general quadratic free energy of the strain $\epsilon$ is $f_\e=\lambda_{ijkl}\epsilon_{ij}\epsilon_{kl}$, but the form of the $\lambda$ tensor is constrained by both that $\epsilon$ is a symmetric tensor and by the point group symmetry \cite{landau_theory_1995}. The latter can be seen in a systematic way. First, the six independent components of strain are written as linear combinations that behave like irreducible representations under the action of the point group, or \begin{equation} \begin{aligned} |